Effective fermion masses of ordergTin high-temperature gauge theories with exact chiral invariance

It is shown that, at finite temperature, chiral invariance does not imply that fermion propagators have poles at K²=0. Instead, a zero-momentum fermion has energy K⁰=M, where M²=g²C(R)T²8 and $C(R)$ is the quadratic Casimir of the fermion representation. The dispersion relation for →K≠0 is computed and can be crudely approximated (to within 10%) by K⁰≈(M²+→K²)1/2. Applications to high-temperature QCD, SU(2)×{}U(1), and grand unified theories are discussed.